4 pages, 1 figure. Contribution to proceedings of QCD 08 Conference, (Montpellier, France, July 7-12, 2008). Modified enunciation of the mapping theorem
发表信息：
Nuclear Physics B (Proc. Suppl.) 186 (2009) 260-263
We present a strong coupling expansion that permits to develop analysis of quantum field theory in the infrared limit. Application to a quartic massless scalar field gives a massive spectrum and the propagator in this regime. We extend the approach to a pure Yang-Mills theory obtaining analogous results. The gluon propagator is compared satisfactorily with lattice results and similarly for the spectrum. Comparison with experimental low energy spectrum of QCD supports the view that $σ$ resonance is indeed a glueball. The gluon propagator we obtained is finally used to formulate a low energy Lagrangian for QCD that reduces to a Nambu-Jona-Lasinio model with all the parameters fixed by those of the full theory.
Correlation functions of Landau gauge Yang-Mills theory are calculated from their equations of motion. Solutions for the three- and four-gluon vertices and the role of two-loop diagrams in the gluon propagator equation are discussed.
We study a manifestly gauge invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in $d=3$ Yang-Mills. The use of the well-known Schwinger mechanism, in the Landau gauge, leads to the dynamical generation of a mass for the gauge boson (gluon in $d=3$), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of $SU(2)$ lattice simulations.
Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both DSE and RGZ results for the ghost propagator is furthermore provided. …
The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. The diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component of the gluon propagator is found to be of the Yukawa type, with a dynamical mass originating from the dimension two condensate <A^2>, which is also taken into account. Finally, the off-diagonal ghost propagator exhibits infrared enhancement.
The Dyson-Schwinger equations of Landau-gauge Yang-Mills theory for the gluon and ghost propagators are investigated. Numerical results are obtained within a truncation scheme which has proven to be successful at vanishing temperature. For temperatures up to 250 MeV we find only minor quantitative changes in the infrared behaviour of the gluon and ghost propagators. The effective action calculated from these propagators is temperature-independent within the numerical uncertainty.
The quenched gluon and ghost propagator data published in [1] is reanalysed following the suggestion of [2] to resolve the differences between the infrared data of the simulations. Our results confirms that the procedure works well either for the gluon or for the ghost propagator but not for both propagators simultaneously as the observed deviations in the data follow opposite patterns. Definitive conclusions require improving the determination of the (ratios) of lattice spacings. A simple procedure for the relative calibration of the lattice spacing in lattice simulations is suggested.
We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the pecularities of the propagators in d=2.
From first principles, using a screened expansion, a simple one-loop analytical expression is provided for the ghost propagator of pure SU(3) Yang-Mills theory in a generic linear covariant gauge. At variance with the Landau gauge, the ghost dressing function is suppressed in the infrared and vanishes at $p=0$, as predicted by other approaches in the continuum. However, in the very limited range where lattice data are available no detectable deviation is found from the Landau gauge, thus reconciling some recent lattice data and previous continuum predictions.
The authors of ref. Phys.Rev. D94 (2016) no.1, 014502 reported about a careful analysis of the impact of lattice artifacts on the $SU(3)$ gauge-field propagators. In particular, they found that the low-momentum behavior of the renormalized propagators depends on the lattice bare coupling and interpreted this fact as the result of it being affected by finite lattice spacing artifacts. We do not share this interpretation and present here a different and more suitable explanation for these results.
Green's functions are gauge-dependent quantities. Thus, the manifestation of confinement in these correlation functions also depends on the gauge. Here we use lattice gauge theory to study the gluon and the ghost propagators in a gauge (the so-called lambda-gauge) interpolating between the Landau and the Coulomb gauge. Results are compared to the usual minimal Landau gauge.
The infrared behavior of the gluon and ghost propagators is studied in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data.
We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter $0<ξ\le 5$. Extrapolating the propagators to $ξ\to \infty $ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values $ξ\lesssim 1/2$ of the gauge fixing parameter. It is shown that the correlation functions, and in par…
We compute ghost and gluon propagators of Yang-Mills theory in the Landau gauge at non-vanishing temperature within a functional renormalisation group setting. We construct purely thermal flows, that project onto thermal fluctuations only. For temperatures and momenta above the confinement-deconfinement temperature Tc the electric propagator shows a thermal suppression due to Debye screening. The magnetic gluon propagator shows a thermal scaling and tends towards the three-dimensional one. In this region both propagators match the lattice propagators. The thermal scaling is also reflected in t…
We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge…
We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case we find D(0) = 0, in agreement with Ref. [1]. We suggest an explanation for these results. We note that our discussion is general, although we only apply our analysis…
The propagators of the elementary degrees of freedom of (minimal-)Landau-gauge Yang-Mills theory have been a useful tool in various investigations. However, in lattice calculations they show severe dependencies on lattice artifacts. This problem has been addressed for various subsets of lattice artifacts and various subsets of propagators over the time. Here, an extended study of all propagators in momentum space, and for the gluon also in position space, as well as derived quantities like the running coupling, is provided simultaneously for two, three, and four dimensions over one or more ord…
G_2 Yang--Mills theory is an interesting laboratory to investigate non-perturbative effects. On one hand, no conventional quark confinement via a linearly rising potential is present. On the other hand, its thermodynamic properties are similar to ordinary SU(N) Yang--Mills theory. Finally, it has been conjectured that gluons are removed from the physical spectrum in the same way as in SU(N) Yang--Mills theory. The last claim will be explored by determining the Landau-gauge ghost and gluon propagators, as well as the Faddeev--Popov operator eigenspectrum, in G_2 lattice gauge theory in two and …
We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to…
We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex expansion of the quantum effective action. Using an exact renormalization group equation, we compute the fully dressed gluon and ghost propagators to lowest nontrivial order in the vertex expansion. In the mid-momentum regime, $p^2\sim\mathcal{O}(1)\text{GeV}^2$, we probe the propagator flow with various {\em ansätze} for the three- and four-point correlations. We analyze the potential of these truncation schemes to generate a nonperturbative scale. We find universal infrared behavior of the propagators, if the gluon …
We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propagator. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agreement with lattice results a…
Yang-Mills theory can be formulated for any semi-simple Lie algebra, and thus any semi-simple Lie group. In principle, the dynamics could be different for each one. However, functional studies predict that the propagators in Landau gauge depend only quantitatively on the gauge algebra. In particular, genuine non-perturbative effects should be present even in the large N-limit for su(N) gauge algebras. Lattice gauge theory is used to investigate this in detail. The propagators are determined for the gauge groups SU(2), SU(3), SU(4), SU(5), SU(6) and G2, in two and three dimensions. In accordanc…
The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to $128^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)$^4$ and $\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators c…
In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoi…
Using the effective potential approach for composite operators, we have analytically evaluated the truly nonperturbative vacuum energy density as obtained by using a model infrared finite gluon propagator which was suggested by lattice simulations. The truly nonperturbative vacuum energy density is defined as the truly nonperturbative part of the full gluon propagator integrated over the deep infrared region (soft momentum region). With this definition, it is a manifestly gauge invariant quantity. We have explicitly shown that the corresponding effective potential has always an imaginary part …
Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N=1 Supersymmetric Yang-Mills (SYM) theory and Minimal Walking Technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N=1 SYM, Minimal Walking Technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to co…
The finite-temperature behavior of gluon and of Faddeev-Popov-ghost propagators is investigated for pure SU(2) Yang-Mills theory in Landau gauge. We present nonperturbative results, obtained using lattice simulations and Dyson-Schwinger equations. Possible limitations of these two approaches, such as finite-volume effects and truncation artifacts, are extensively discussed. Both methods suggest a very different temperature dependence for the magnetic sector when compared to the electric one. In particular, a clear thermodynamic transition seems to affect only the electric sector. These results…
Yang-Mills theories undergo a deconfining phase transition at a critical temperature. In lattice calculations the temporal Wilson loop and Z_3 order parameter show above this temperature a behavior typical of deconfinement. A quantity of interest in the study of this transition is the gluon propagator and its evolution with temperature. This contribution describes the current status of an investigation of the finite temperature gluon propagator in Landau gauge. It analyzes the high temperature case. The resulting equations are compared to the corresponding ones of three-dimensional Yang-Mills …
We present approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang-Mills theories. We solve the corresponding Dyson-Schwinger equations in flat Euclidean space-time without any angular approximation. This supplements recently obtained results employing a four-torus, i.e. a compact space-time manifold, as infrared regulator. We confirm previous findings deduced from an extrapolation with tori of different volumes: the gluon propagator is weakly vanishing in the infrared and the ghost propagator is highly singular. For non-vanishing momenta …
The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate <A^2> is also considered. In this case, the transvers…
Recent works have explored non-perturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a non-trivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Inhere, we res…
The Cucchieri-Mendes bounds for the gluon propagator are discussed for the four dimensional pure gauge SU(3) theory. Assuming a pure power law dependence on the inverse of the lattice volume, the lattice data gives a vanishing zero momentum gluon propagator in the infinite volume limit. Our investigation shows that this result is robust against variations of the lattice volumes and corrections to the power law. Moreover, it is consistent with the Gribov-Zwanziger horizon condition and contradicts the SU(2) analysis, which assumed the same type of dependence on the inverse of the volume. Our an…
We present non-perturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.
We examine the possibility that there may exist a logarithmic correction to the infrared asymptotic solution with power behavior which has recently been found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We propose a new Ansatz to find a pair of solutions for the gluon and ghost form factors by solving the coupled Schwinger-Dyson equation under a simple truncation. This Ansatz enables us to derive the infrared and ultraviolet asymptotic solutions simultaneously and to understand why the power solution and the logarithmic solution is possible only in the infrared and u…
We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic mon…
We study the Landau gauge gluon propagators in dense two-color QCD at quark chemical potential, $μ_q$, in the range from 0.5 to 1.0 GeV not reachable by the perturbative method at weak coupling. In order to take into account the non-perturbative effects, at tree level we use a massive Yang-Mills model for the Yang-Mills theory (or the Curci-Ferrari model) which has successfully described the lattice results of the gluon and ghost propagators in the Landau gauge. We couple quarks to this theory and compute the one-loop polarization effects in medium. The presence of the gluon mass significantly…
The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge p…
We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-tim…
Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a non-trivial problem due to the presence of Gribov copies. In particular, there are different gauges in the non-perturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal and absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigati…
We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model ansaetze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propag…
We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau-gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two dim…
Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view to deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the BRS invariance and it is found that there exists two forms of invariance - invariance under the standard BRS transform and under a second, non-standard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the non-stan…
The Yang-Mills Schrödinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.
The exact nonperturbative confining solutions of the SU(3)-Yang-Mills equations recently obtained by author in Minkowski spacetime with the help of the black hole theory techniques are analysed and on the basis of them the gluon propagator corresponding to linear confinement at large distances (small momenta) is constructed in a nonperturbative way. At small distances (large momenta) the resulting propagator passes on to the standard (nonperturbative) gluon propagator used in the perturbative quantum chromodynamics (QCD). The results suggest some scenario of linear confinement for mesons and q…
The infrared behaviour of gluon and ghost propagators, ghost-gluon vertex and three-gluon vertex is investigated for both the covariant Landau and the non-covariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behaviour of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the C…
We investigate the infrared (strong-coupling) regime of SU(N)-Yang-Mills theory on a self-dual background. We present an evaluation of the full effective potential for the field strength invariant F_{μν}F^{μν} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the beta function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators. Consistency between both gauges in the infrared …
In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis of the infrared asymptotics of propagators in any spatial dimension follows, and a connection to the Landau gauge is given. In the Coulomb gauge Hamiltonian approach, a linearly rising static color Coulomb potential is found, along with an infrared diverging gluon energy, both signaling confinement. The propagators and vertices in the entire momentum regime are calculated with the variational principle.…
The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite volume effects affecting these Green's functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dy…
We demonstrate that power-like non-perturbative behavior of gluon and ghost propagators in infrared limit of Yang-Mills theories can provide at finite temperatures T a negative T^4-contribution to the pressure and energy density. Existence of mass gap implies then new relations between infrared critical exponents of gluon and ghost propagators.
By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in Landau gauge) in the low momentum regime and to give rise to an OPE correction to the latter of ${\sqrtσ}/{p^3}$.The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase tran…
We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs from lattice simulations. We show that lattice data are in serious conflict with a widely spread analytical relation between the gluon and ghost infrared critical exponents. We conjecture that this is explained by a singular behaviour of the ghost-ghost-gluon vertex function in the infrared. We show…
Using the effective potential approach for composite operators, we have formulated a general method of calculation of the truly nonperturbative Yang-Mills vacuum energy density in the covariant gauge QCD ground state quantum models. It is defined as an integration of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). A nontrivial minimization procedure makes it possible to determine the value of the soft cutoff in terms of the corresponding nonperturbative scale parameter, which is inevitably present in any nonperturbative model fo…
In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $ξ$ in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $ξ>0$ are infrared finite, as is the case in the Landau gauge $(ξ=0)$. Then we appeal to the Nielsen identities, and expre…
In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative inner product. In this work we demonstrate that for quantum chromodynamics (QCD) this constraint gives rise to an interconnection between the ghost and gluon spectra, and in doing so provides a non-trivial test of whether BRST symmetry is realised no…
Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex dynamically. In the gluon propagator also two-loop diagrams are taken into account. The higher gluonic correlation functions show sizable deviations from the tree-level only at low momenta. Also the couplings derived from the vertices agree well down to a few GeV. In addition, different methods to subtract spurious divergences are explored.
We present results for the gluon and ghost propagators and the ghost-gluon vertex obtained from Dyson-Schwinger equations. In the zero temperature case we elaborate on the role of the three-gluon vertex and discuss a model that can capture its qualitative features like its anomalous dimensions and a zero crossing of the dressing function. Our results compare well with lattice data. At non-zero temperature we calculated the ghost propagator which agrees rather well with lattice results already within our simple truncation. These results are used to obtain the temperature dependence of the ghost…
We derive a gauge-invariant low-energy effective model of the Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type and agrees with it when a mass term which breaks nilpotency of the BRST symmetry is included. We show that the effective model with gluon propagator of the Gribov-Stingl type exhibits both quark and gluon confinement: the Wilson loop average has the area law and the Schwinger function violates reflection positivity. However, we argue that both quark and gluon confinement can be obtained even in the absence of such a mass term.
We evaluate the longitudinal or (chromo-)electric Yang-Mills gluon propagator in the recently proposed center-symmetric Landau gauge at finite temperature [1]. To model the effect of the Gribov copies in the infrared, we use the Curci-Ferrari model which, in turn, allows us to rely on perturbative calculations. At one-loop order in the SU(2) case, the so-obtained longitudinal gluon propagator provides a clear signature for Z2 center-symmetry breaking with a singular behavior, characteristic of a continuous phase transition. This is in sharp contrast with what is found within the standard Landa…
Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mil…
We derive a gauge-invariant low-energy effective model of the SU(2) Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type, irrespective of the gauge choice. In the maximally Abelian gauge, especially, we demonstrate that the model exhibits both quark confinement and gluon confinement: the Wilson loop average has area law and the Schwinger function violates reflection positivity. Moreover, we give a formula for the string tension calculable from the gluon propagator of the gauge-invariant field strength and gives a good estimate for the string tension.…
